In this paper, numerical techniques are developed
for solving two-dimensional Bratu equations using different
neural network models optimized with the sequential quadratic
programming technique. The original two-dimensional problem
is transformed into an equivalent singular, nonlinear boundary
value problem of ordinary differential equations. Three neural
network models are developed for the transformed problem
based on unsupervised error using log-sigmoid, radial basis and
tan-sigmoid functions. Optimal weights for each model are
trained with the help of the sequential quadratic programming
algorithm. Three test cases of the equation are solved using the
proposed schemes. Statistical analysis based on a large number
of independent runs is carried out to validate the models in terms
of accuracy, convergence and computational complexity.
کلید واژگان :
Two-dimensional Bratu equations Neural networks Sequential quadratic programming Boundary value problems Nonlinear singular system
